Stability of the global ocean circulation: Basic bifurcation diagrams

A study of the stability of the global ocean circulation is performed within a coarse-resolution general circulation model. Using techniques of numerical bifurcation theory, steady states of the global ocean circulation are explicitly calculated as parameters are varied. Under a freshwater flux forcing that is diagnosed from a reference circulation with Levitus surface salinity fields, the global ocean circulation has no multiple equilibria. It is shown how this unique-state regime transforms into a regime with multiple equilibria as the pattern of the freshwater flux is changed in the northern North Atlantic Ocean. In the multiple-equilibria regime, there are two branches of stable steady solutions: one with a strong northern overturning in the Atlantic and one with hardly any northern overturning. Along the unstable branch that connects both stable solution branches (here for the first time computed for a global ocean model), the strength of the southern sinking in the South Atlantic changes substantially. The existence of the multiple-equilibria regime critically depends on the spatial pattern of the freshwater flux field and explains the hysteresis behavior as found in many previous modeling studies.